Nitrogen (N) contamination within agricultural‐karst landscapes and aquifers is widely reported; however, the complex hydrological pathways of karst make N fate difficult to ascertain. We developed a hydrologic and N numerical model for agricultural‐karst, including simulation of soil, epikarst, phreatic, and quick flow pathways as well as biochemical processes such as nitrification, mineralization, and denitrification. We tested the model on four years of nitrate (NO3−) data collected from a phreatic conduit and an overlying surface channel in the Cane Run watershed, Kentucky, USA. Model results indicate that slow to moderate flow pathways (phreatic and epikarst) dominate the N load and account for nearly 90% of downstream NO3− delivery. Further, quick flow pathways dilute NO3− concentrations relative to background aquifer levels. Net denitrification distributed across soil, epikarst, and phreatic water removes approximately 36% of the N inputs to the system at rates comparable to nonkarst systems. Evidence is provided by numerical modeling that NO3− accumulation via evapotranspiration in the soil followed by leaching through the epikarst acts as a control on spring NO3− concentration and loading. Compared to a fluvial‐dominated immature karst system, mature‐karst systems behave as natural detention basins for NO3−, temporarily delaying NO3− delivery to downstream waters and maintaining elevated NO3− concentrations for days to weeks after hydrologic activity ends. This study shows the efficacy of numerical modeling to elucidate complex pathways, processes, and timing of N in karst systems.

Nutrient dynamics in karst agroecosystems remain poorly understood, in part due to limited long-term nested datasets that can discriminate upland and in-stream processes. We present a 10-year dataset from a karst watershed in the Inner-Bluegrass Region of central Kentucky, consisting of nitrate (nitrate-N [NO 3 − ]), dissolved reactive phosphorus (DRP), total organic carbon (TOC), and total ammoniacal-N (TAN) measurements at nested spring and stream sites as well as flowrate at the watershed outlet. Hydrograph separation techniques were coupled with multiple linear regression and Empirical Mode Decomposition time-series analysis to determine significance of seasonal processes and to generate continuous estimates of nutrient pathway loadings. Further, we used model results of benthic algae growth and decomposition dynamics from a nearby watershed to assess if transient storage in algal biomass could explain differences in spring and downstream watershed nutrient loading. Results highlight statistically significant seasonality for all nutrients at stream sites, but only for NO 3 − at springs with longitudinal variability showing significant decreases occurring from spring to stream sites for NO 3 − and DRP, and significant increases for TOC and TAN. Pathway loading analysis highlighted the importance of slow flow pathways to source approximately 70% of DRP and 80% of NO 3 − . Results for in-stream dynamics suggest that benthic autotroph dynamics can explain summer deviations for TOC, TAN, and DRP but not NO 3 − . Regarding upland dynamics, our findings agree well with existing perceptions in karst for N pathways and upland source seasonality but deviate from perceptions that karst conduits are retentive of P, reflecting the limited buffering capacity of the soil profile and conduit sediments in the Inner-Bluegrass. Regarding in-stream fate, our findings highlighted the significance of seasonally driven nutrient processing in the bedrock-controlled streambed to influence nutrient fluxes at the watershed outlet. Contrary to existing perceptions, we found high N attenuation and an unexplained NO 3 − sink in the bedrock stream, leading us to postulate that floating macrophytes facilitate high rates of denitrification. KEYWORDS bedrock stream, hydrologic pathways, in-stream fate, karst agroecosystem watershed, nutrient loadings, time-series analysis

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Excessive nitrate threatens a wide range of water resources, aquatic habitats, and sensitive infrastructure. Despite this problem, tracing a nutrient from its eventual fate back to its origin remains an elusive challenge due to heterogeneity in how nutrient sources and hydrologic pathways are connected. Typically, this problem is underdetermined (i.e., too many unknowns, not enough equations) and cannot be solved with existing methodologies. The theory of optimal transport allows for the solution of underdetermined systems, and here we construct a novel formulation for its use in water quality modeling. Our objective was to develop an optimal transport modeling framework-coupled to Bayesian source unmixing, loadograph pathway separation, and geospatial connectivity analysis-to apportion nitrate loading from three sources (soil, fertilizer, and manure) across three pathways (quick, intermediate, and slow), resulting in nine possible source-pathway couplings (soil-quick, soil-intermediate, …, manure-slow). We apply this model to a 30 month elemental (NO 3 −) and isotopic (δ 15 N and δ 18 O) nitrate data set from a karst watershed in Kentucky, USA. Modeling results indicate that-of the nine possible source-pathway couplings-nearly 60% of nitrate export is facilitated by just three: fertilizer-quick (16.4%), manure-intermediate (15.4%), and soil-slow (27.2%). Further, we reinforce the need to explicitly consider heterogeneity in source-pathway connectivity as homogeneous assumptions lead to erroneous inferences. The applicability of the model, its input requirements, and transferability to other sites is discussed. Lastly, we simulated two land management scenarios (field buffers and septic repair) and demonstrate how optimal transport can be used to test nutrient reduction strategies.

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